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A Broad Grid of 2D Kilonova Emission Models

Depending upon the properties of their compact remnants and the physics included in the models, simulations of neutron star mergers can produce a broad range of ejecta properties. The characteristics of this ejecta, in turn, define the kilonova emission. To explore the effect of ejecta properties, we present a grid of 2-component 2D axisymmetric kilonova simulations that vary mass, velocity, morphology, and composition. The masses and velocities of each component vary, respectively, from 0.001 to 0.1 M ⊙ and 0.05 to 0.3c, covering much of the range of results from the neutron star merger literature. The set of 900 models is constrained to have a toroidal low electron fraction (Y e ) ejecta with a robust r-process composition and either a spherical or lobed high-Y e ejecta with two possible compositions. We simulate these models with the Monte Carlo radiative transfer code SuperNu using a full suite of lanthanide and 4th row element opacities. We examine the trends of these models with parameter variation, show how it can be used with statistical tools, and compare the model light curves and spectra to those of AT2017gfo, the electromagnetic counterpart of GW170817.

79 ASTRONOMY AND ASTROPHYSICS↗

Constraining Inputs to Realistic Kilonova Simulations through Comparison to Observed r -process Abundances

Kilonovae, one source of electromagnetic emission associated with neutron star mergers, are powered by the decay of radioactive isotopes in the neutron-rich merger ejecta. Models for kilonova emission consistent with the electromagnetic counterpart to GW170817 predict characteristic abundance patterns, determined by the relative balance of different types of material in the outflow. Assuming that the observed source is prototypical, this inferred abundance pattern in turn must match r -process abundances deduced by other means, such as what is observed in the solar system. We report on analysis comparing the input mass-weighted elemental compositions adopted in our radiative transfer simulations to the mass fractions of elements in the Sun, as a practical prototype for the potentially universal abundance signature from neutron star mergers. We characterize the extent to which our parameter inference results depend on our assumed composition for the dynamical and wind ejecta and examine how the new results compare to previous work. We find that a dynamical ejecta composition calculated using the FRDM2012 nuclear mass and FRLDM fission models with extremely neutron-rich ejecta ($Y_e$ = 0.035) along with moderately neutron-rich ($Y_e$ = 0.27) wind ejecta composition yields a wind-to-dynamical mass ratio of $M_w$/$M_d$ = 0.47, which best matches the observed AT2017gfo kilonova light curves while also producing the bestmatching abundance of neutron capture elements in the solar system, though, allowing for systematics, the ratio may be as high as of order unity.

79 ASTRONOMY AND ASTROPHYSICS↗

Physics-driven Explosions of Stripped High-mass Stars: Synthetic Light Curves and Spectra of Stripped-envelope Supernovae with Broad Light Curves

Stripped-envelope supernovae (SESNe) represent a significant fraction of core-collapse supernovae, arising from massive stars that have shed their hydrogen and, in some cases, helium envelopes. The origins and explosion mechanisms of SESNe remain a topic of active investigation. In this work, we employ radiative-transfer simulations to model the light curves and spectra of a set of explosions of single, solar-metallicity, massive Wolf–Rayet stars with ejecta masses ranging from 4 to 11 M ⊙ , which were computed from a turbulence-aided and neutrino-driven explosion mechanism. We analyze these synthetic observables to explore the impact of varying ejecta mass and helium content on observable features. We find that the light curve shape of these progenitors with high ejecta masses is consistent with observed SESNe with broad light curves but not the peak luminosities. The commonly used analytic formula based on rising bolometric light curves overestimates the ejecta mass of these high-initial-mass progenitor explosions by a factor of up to 2.6. In contrast, the calibrated method by Haynie et al., which relies on late-time decay tails, reduces uncertainties to an average of 20% within the calibrated ejecta mass range. Spectroscopically, the He I 1.083 μm line remains prominent even in models with as little as 0.02 M ⊙ of helium. However, the strength of the optical He I lines is not directly proportional to the helium mass but instead depends on a complex interplay of factors such as the 56 Ni distribution, composition, and radiation field. Thus, producing realistic helium features requires detailed radiative transfer simulations for each new hydrodynamic model.

79 ASTRONOMY AND ASTROPHYSICS↗

Combining visible shadowgraph imaging with x-ray imaging for dynamic shock experiments

Interrogating ejecta particles launched from target materials that are undergoing dynamic shock can be done with both x-ray imaging and visible shadowgraph imaging. Our dynamic testing must be done inside a containment vessel with limited access ports available. We designed an imaging system to relay both types of imaging systems through a single port using the same optical relay and then splitting the images onto three separate high-speed imaging cameras outside the containment vessel. X-ray imaging provides ejecta density measurements. Shadowgraph imaging that is done at two wavelengths (blue and red) constrains ejecta particle size distributions and provides areal density measurements of the ejecta cloud. The ejecta particles are positioned 225 mm before the x-ray scintillators; this arrangement permits a folded mirror system to allow the shadowgraph data to bypass the x-ray scintillators. This configuration results in spatial separations between the intermediate image planes of the x-ray and shadowgraph images along the optical axis. At the position of the x-ray intermediate image plane, mirrors are positioned such that the shadowgraph images are kicked out and their images are sent on to different cameras. Positioning of the large doublet relay lenses keeps shrapnel from impacting the vessel containment windows.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

AT2017gfo: Bayesian inference and model selection of multicomponent kilonovae and constraints on the neutron star equation of state

The joint detection of the gravitational wave GW170817, of the short γ-ray burst GRB170817A and of the kilonova AT2017gfo, generated by the the binary neutron star (NS) merger observed on 2017 August 17, is a milestone in multimessenger astronomy and provides new constraints on the NS equation of state. We perform Bayesian inference and model selection on AT2017gfo using semi-analytical, multicomponents models that also account for non-spherical ejecta. Observational data favour anisotropic geometries to spherically symmetric profiles, with a log-Bayes’ factor of ~104, and favour multicomponent models against single-component ones. The best-fitting model is an anisotropic three-component composed of dynamical ejecta plus neutrino and viscous winds. Using the dynamical ejecta parameters inferred from the best-fitting model and numerical–relativity relations connecting the ejecta properties to the binary properties, we constrain the binary mass ratio to q < 1.54 and the reduced tidal parameter to $120\lt \tilde{\Lambda }\lt 1110$. Finally, we combine the predictions from AT2017gfo with those from GW170817, constraining the radius of a NS of 1.4 M ⊙ to 12.2 ± 0.5 km (1σ level). This prediction could be further strengthened by improving kilonova models with numerical-relativity information.

79 ASTRONOMY AND ASTROPHYSICS↗

The Lick Observatory Supernova Search follow-up program: photometry data release of 70 SESNe

We present BVRI and unfiltered (Clear) light curves of 70 stripped-envelope supernovae (SESNe), observed between 2003 and 2020, from the Lick Observatory Supernova Search follow-up program. Our SESN sample consists of 19 spectroscopically normal SNe Ib, 2 peculiar SNe Ib, six SNe Ibn, 14 normal SNe Ic, 1 peculiar SN Ic, 10 SNe Ic-BL, 15 SNe IIb, 1 ambiguous SN IIb/Ib/c, and 2 superluminous SNe. Our follow-up photometry has (on a per-SN basis) a mean coverage of 81 photometric points (median of 58 points) and a mean cadence of 3.6 d (median of 1.2 d). From our full sample, a subset of 38 SNe have pre-maximum coverage in at least one passband, allowing for the peak brightness of each SN in this subset to be quantitatively determined. We describe our data collection and processing techniques, with emphasis toward our automated photometry pipeline, from which we derive publicly available data products to enable and encourage further study by the community. Using these data products, we derive host-galaxy extinction values through the empirical colour evolution relationship and, for the first time, produce accurate rise-time measurements for a large sample of SESNe in both optical and infrared passbands. By modelling multiband light curves, we find that SNe Ic tend to have lower ejecta masses and lower ejecta velocities than SNe Ib and IIb, but higher 56Ni masses.

Lick Observatory↗

Progenitors and explosion properties of supernova remnants hosting central compact objects: II. A global systematic study with a comparison to nucleosynthesis models

ABSTRACT Core-collapse explosions of massive stars leave behind neutron stars, with a known diversity that includes the ‘Central Compact Objects’ (CCOs). Typified by the neutron star discovered near the centre of the Cas A supernova remnant (SNR), CCOs have been observed to shine only in X-rays. To address their supernova progenitors, we perform a systematic study of SNRs that contain a CCO and display X-ray emission from their shock-heated ejecta. We make use of X-ray data primarily using the Chandra X-ray observatory, complemented with XMM–Newton. This study uses a systematic approach to the analysis of each SNR aimed at addressing the supernova progenitor as well as the explosion properties (energy and ambient density). After fitting for the ejecta abundances estimated from a spatially resolved spectroscopic study, we compare the data to six nucleosynthesis models making predictions on supernova ejecta yields in core-collapse explosions. We find that the explosion models commonly used by the astrophysics community do not match the ejecta yields for any of the SNRs, suggesting additional physics, for example multidimensional explosion models or updated progenitor structures, are required. Overall we find low-mass (≤25 solar masses) progenitors among the massive stars population and low-energy explosions (<1051 ergs). We discuss degeneracies in our model fitting, particularly how altering the explosion energy affects the estimate of the progenitor mass. Our systematic study highlights the need for improving on the theoretical models for nucleosynthesis predictions as well as for sensitive, high-resolution spectroscopy observations to be acquired with next generation X-ray missions.

79 ASTRONOMY AND ASTROPHYSICS↗

Long-lived neutron-star remnants from asymmetric binary neutron star mergers: element formation, kilonova signals and gravitational waves

We present 3D general-relativistic neutrino-radiation hydrodynamics simulations of two asymmetric binary neutron star mergers producing long-lived neutron stars remnants and spanning a fraction of their cooling time scale. The mergers are characterized by significant tidal disruption with neutron rich material forming a massive disc around the remnant. The latter develops one-armed dynamics that is imprinted in the emitted kilo-Hertz gravitational waves. Angular momentum transport to the disc is initially driven by spiral-density waves and enhanced by turbulent viscosity and neutrino heating on longer timescales. The mass outflows are composed by neutron-rich dynamical ejecta of mass ∼10 −3 –10 −2 M ⊙ followed by a persistent spiral-wave/neutrino-driven wind of ≳ 10 −2 M ⊙ with material spanning a wide range of electron fractions, ∼0.1–0.55. Dynamical ejecta (winds) have fast velocity tails up to ∼0.8 (∼0.4) c. The outflows are further evolved to days timescale using 2D ray-by-ray radiation-hydrodynamics simulations that include an online nuclear network. We find complete r-process yields and identify the production of 56 Ni and the subsequent decay chain to 56 Co and 56 Fe. Synthetic kilonova light curves predict an extended (near-) infrared peak a few days postmerger originating from r-process in the neutron-rich/high-opacity ejecta and UV/optical peaks at a few hours (ten minutes) postmerger originating from weak r-process (free-neutron decay) in the faster ejecta components. Additionally, the fast tail of tidal origin generates kilonova afterglows potentially detectable in radio and X band on a few to ten years time scale. Quantitative effects originating from the tidal disruption merger dynamics are reflected in the multimessenger emissions.

abundances↗

2D end-to-end modelling of kilonovae from binary neutron star merger remnants

We investigate the kilonova emission resulting from outflows produced in a 3D general-relativistic magnetohydrodynamic (GRMHD) simulation of a hypermassive neutron star (HMNS) remnant. We map the outflows into the flash hydrodynamics code to model their expansion in axisymmetry, and study the effects of employing different r-process heating rates. Except for the highest heating rate prescription, we find no significant differences with respect to overall ejecta dynamics and morphology compared to the simulation without heating. Once homologous expansion is attained, typically after ~2s for these ejecta, we map the outflows to the sedona radiative transfer code and compute the spectral evolution of the kilonova and broad-band light curves in various Legacy Survey of Space and Time (LSST) bands. The kilonova properties depend on the remnant lifetime, with peak luminosities and peak time-scales increasing for longer lived remnants that produce more massive ejecta. For all models, there is a strong dependence of both the bolometric and broad-band light curves on the viewing angle. While the short-lived (12 ms) remnant produces higher luminosities when viewed from angles closer to the pole, longer lived remnants (240 ms and 2.5 s) are more luminous when viewed from angles closer to the equator. Our results highlight the importance of self-consistent, long-term modelling of merger ejecta, and taking viewing-angle dependence into account when interpreting observed kilonova light curves. We find that magnetized outflows from an HMNS – if it survives long enough – could explain blue kilonovae, such as the blue emission seen in AT2017gfo.

79 ASTRONOMY AND ASTROPHYSICS↗

Gamma-ray signatures of 𝑟-process radioactivity from the collapse of magnetized white dwarfs

We predict the gamma-ray line emission from 𝑟-process nuclei synthesized in the ejecta of the accretion-induced collapse (AIC) of a magnetized, rapidly rotating white dwarf. Using ejecta from a two-dimensional general-relativistic neutrino-magnetohydrodynamic simulation, further evolved with a radiation-hydrodynamics code coupled to an in situ nuclear reaction network, we construct angle-dependent gamma-ray spectra in the 0.01–10 MeV band via composition-dependent ray tracing through the ejecta. The emission between ∼1 and 10 d is dominated by 132 I (𝑡 1/2 = 2.3 h), continuously replenished by the decay of its parent 132 Te (𝑡 1/2 = 3.2 d), with additional contributions from 131 I, 133 Xe, and 132 Te . At 𝑡 ≳ 20 d, 56 Co (from 56 Ni decay) becomes the primary emitter. The simultaneous presence of 𝑟 process and iron-peak gamma-ray lines is distinctive of AIC ejecta and absent in binary neutron star mergers, where iron-peak nuclei are generally not synthesized. Comparing with the 3⁢𝜎 continuum sensitivities of planned MeV gamma-ray telescopes (COSI, AMEGO-X, e-ASTROGAM, GRAMS, GammaTPC), we find the brightest 𝑟-process lines detectable to ∼10 Mpc by GammaTPC and GRAMS, with the signal approaching their sensitivity threshold at 30 Mpc. As a result, the 𝑟-process spectral features survive time integration over ∼30 d exposures, demonstrating robustness against the long observation times required by gamma-ray detectors.

Nuclear reactions↗

Gamma Rays from Kilonova: A Potential Probe of r-process Nucleosynthesis

The mergers of compact binaries with at least one neutron star component are the potential leading sites of the production and ejection of r-process elements. Discoveries of galactic binary pulsars, short gamma-ray bursts, and gravitational-wave detections have all been constraining the rate of these events, while the gravitational wave plus broadband electromagnetic coverage of binary neutron star merger (GW170817) has also placed constraints on the properties (mass and composition) of the merger ejecta. But uncertainties and ambiguities in modeling the optical and infrared emission make it difficult to definitively measure the distribution of heavy isotopes in these mergers. In contrast, gamma rays emitted in the decay of these neutron-rich ejecta may provide a more direct measurement of the yields. We calculate the gamma production in remnants of neutron star mergers, considering two epochs: a kilonova epoch, lasting about two weeks, and a much later epoch of tens and hundreds of thousands of years after the merger. For the kilonova epoch, when the expanding ejecta is still only partially transparent to gamma radiation, we use 3D radiative transport simulations to produce the spectra. Futhermore, we show that the gamma-ray spectra associated with beta- and alpha-decay provide a fingerprint of the ejecta properties and, for a sufficiently nearby remnant, may be detectable, even for old remnants. We compare our gamma spectra with the potential detection limits of next generation detectors, including the Lunar Occultation Explorer (LOX), the All-sky Medium Energy Gamma-ray Observatory (AMEGO), and the Compton Spectrometer and Imager (COSI). We show that fission models can be discriminated via the presence of short-lived fission fragments in the remnant spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

The Spectacular Ultraviolet Flash from the Peculiar Type Ia Supernova 2019yvq

Early observations of Type Ia supernovae (SNe Ia) provide essential clues for understanding the progenitor system that gave rise to the terminal thermonuclear explosion. Here, we present exquisite observations of SN 2019yvq, the second observed SN Ia, after iPTF 14atg, to display an early flash of emission in the ultraviolet (UV) and optical. Our analysis finds that SN 2019yvq was unusual, even when ignoring the initial flash, in that it was moderately underluminous for a SN Ia ($M_g \approx -18.5$ mag at peak) yet featured very high absorption velocities ($v \approx 15,0000$ km s -1 for Si II λ6355 at peak). We find that many of the observational features of SN 2019yvq, aside from the flash, can be explained if the explosive yield of radioactive 56 Ni is relatively low (we measure $M_{^{56}\mathrm{Ni}} = 0.31 \pm 0.05\,M_\odot$) and it and other iron-group elements are concentrated in the innermost layers of the ejecta. To explain both the UV/optical flash and peak properties of SN 2019yvq we consider four different models: interaction between the SN ejecta and a nondegenerate companion, extended clumps of 56 Ni in the outer ejecta, a double-detonation explosion, and the violent merger of two white dwarfs. Each of these models has shortcomings when compared to the observations; it is clear additional tuning is required to better match SN 2019yvq. In closing, we predict that the nebular spectra of SN 2019yvq will feature either H or He emission, if the ejecta collided with a companion, strong [Ca II] emission, if it was a double detonation, or narrow [O I] emission, if it was due to a violent merger.

79 ASTRONOMY AND ASTROPHYSICS↗

Particle-in-cell Simulations of Mildly Relativistic Outflows in Kilonova Emissions

Abstract The electromagnetic emission from neutron star mergers is comprised of multiple components. Synchrotron emission from the disk-powered jet and thermal emission from the merger ejecta (powered by a variety of sources) are among the most studied sources. The low masses and high velocities of the merger ejecta quickly develop conditions where emission from collisionless shocks becomes critical and synchrotron emission from the merger ejecta constitutes a third component to the observed signal. The aim of this project is to examine shock development, magnetic field generation, and particle acceleration in the case of mildly relativistic shocks, which are expected when the tidal ejecta of neutron star mergers drive a shock into the external medium. Using LANL’s vector particle-in-cell (VPIC) code, we have run simulations of such mildly relativistic, collisionless, weakly magnetized plasmas and computed the resultant magnetic fields and particle energy spectra. We show the effects of varying plasma conditions, as well as explore the validity of using different proton-to-electron mass ratios in VPIC. Our results have implications for observing late-time electromagnetic counterparts to gravitational wave detections of neutron star mergers.

79 ASTRONOMY AND ASTROPHYSICS↗

The Landscape of Thermal Transients from Supernovae Interacting with a Circumstellar Medium

The interaction of supernova ejecta with a surrounding circumstellar medium (CSM) generates a strong shock, which can convert ejecta kinetic energy into observable radiation. Given the diversity of potential CSM structures (arising from diverse mass-loss processes such as late-stage stellar outbursts, binary interaction, and winds), the resulting transients can display a wide range of light-curve morphologies. We provide a framework for classifying the transients arising from interaction with a spherical CSM shell. The light curves are decomposed into five consecutive phases, starting from the onset of interaction and extending through shock breakout and subsequent shock cooling. The relative prominence of each phase in the light curve is determined by two dimensionless quantities representing the CSM-to-ejecta mass ratio η, and the breakout parameter ξ. These two parameters define four light-curve morphology classes, where each class is characterized by the location of the shock breakout and the degree of deceleration as the shock sweeps up the CSM. We compile analytic scaling relations connecting the luminosity and duration of each light-curve phase to the physical parameters. We then run a grid of radiation hydrodynamics simulations for a wide range of ejecta and CSM parameters to numerically explore the landscape of interaction light curves, and to calibrate and confirm the analytic scalings. We connect our theoretical framework to several case studies of observed transients, highlighting the relevance in explaining slow-rising and superluminous supernovae, fast blue optical transients, and double-peaked light curves.

79 ASTRONOMY AND ASTROPHYSICS↗

Simulation to a Newborn Supernova Remnant from a Low-mass Iron Core Star

Supernova remnant observations show a high degree of asymmetry, mixing, and inhomogeneity. These asymmetries are seeded during the early seconds of the explosion and are further enhanced and modified as the shock and ejecta move through the stellar progenitor and into the circumstellar medium. We present simulations of a 9.6 M⊙ zero-metallicity progenitor initialized after shock revival and evolved for several years when the ejecta is in the circumstellar medium. A suite of 1D and 2D simulations examines the effects of neutron-star wind and radioactive decay heating. In 1D, decay heating forms a low-density bubble that suppresses the reverse shock. While in 2D, the heating is localized to metal-rich pockets, inflating them and compressing the surrounding material into dense shells. In 3D, the neutron-star wind and decay heating modify the plume morphology, producing more large-scale structures. The extended plume morphology leads to an asymmetrical shock breakout. After breakout, the leading plumes cannot keep up with the shock front, resulting in deceleration and fragmentation by the reverse shock while retaining the large-scale asymmetry. The projected ejecta morphology and velocities are strongly viewing angle dependent. The relatively uniform metal-rich distribution does not resemble the strongly inhomogeneous ejecta structure of Cas A. The 160-isotope decay network shows that 24.4% of the radioactive heating comes from decay chains other than the canonical 56Ni chain. The low explosion energy, low 56Ni yield, and Ni/Fe ratio greater than unity suggest an observational signature similar to an electron capture supernova.

Neopane, Sudarshan [University of Tennessee (UT)]↗

Generalizing the compressible pairwise interaction extended point-particle model

Ejecta physics plays an important role in material interfaces that are impacted by a strong shock wave. When a shock impacts a rough surface of solid material and melts it, the Richtmyer–Meshkov instability grows perturbations on the surface, which can eject particles. After release, the ejecta travel through the post-shock compressible flow. To accurately simulate a large number of ejecta particles, an Euler–Lagrange approach is preferred, which requires modeling the subgrid-scale physics involved with fluid–particle interactions. We generalize the previous work from Hsiao et al. (2023) to consider systems of moving particles subject to any loading shock. The following improvements were made: (1) Particles are allowed to move relative to each other (2) Non-planar shocks are accounted for along with allowing for variable shock speeds. As a result, the generalized algorithm was tested with particle-resolved simulations for canonical test cases. The results of these tests are discussed and analyzed.

97 MATHEMATICS AND COMPUTING↗

Revealing the Moon's Taurus‐Littrow Landslide via Integrated Analysis of Pristine Apollo 17 Soil Core 73001/2

The “light mantle” deposit at the base of South Massif in the Moon's Taurus‐Littrow Valley was a primary science target for the Apollo 17 exploration. The possibility that it was a landslide triggered by ejecta from Tycho Crater is critical for establishing the age of Tycho and constraining recent lunar impact chronology; however, the mechanism of emplacement of the deposit has recently been questioned. The newly opened 73001/73002 double drive tube from Station 3 sampled 70.6 cm deep into the regolith and represents the first stratigraphic section of an extraterrestrial landslide deposit returned to Earth. Here we provide an overview of the stratigraphy of the 73001/73002 core based on top to bottom variations revealed by coordinated laboratory analyses and explore constraints on the emplacement of the light mantle deposit. Briefly, the upper ∼10 cm of 73002 contains a disturbed zone from space weathering and emplacement of ejecta from a nearby crater that excavated and ejected basaltic material. Below 10 cm is a nearly uniform unit of immature regolith. These data support a single event for the emplacement of the deposit at this location, followed by weathering and mixing of materials from nearby crater ejecta in the upper 10 cm. Slight variations in chemistry and clast components may reflect the relative stratigraphy of the South Massif slope, with material toward the bottom of 73001 originating from lower slopes and material from higher up in the core representing regolith from higher up the South Massif slopes.

58 GEOSCIENCES↗

Late-time post-merger modeling of a compact binary: effects of relativity, r-process heating, and treatment of transport

Detectable electromagnetic counterparts to gravitational waves from compact binary mergers can be produced by outflows from the black hole-accretion disk remnant during the first 10 s after the merger. Two-dimensional axisymmetric simulations with effective viscosity remain an efficient and informative way to model this late-time post-merger evolution. In addition to the inherent approximations of axisymmetry and modeling turbulent angular momentum transport by a viscosity, previous simulations often make other simplifications related to the treatment of the equation of state and turbulent transport effects. In this paper, we test the effect of these modeling choices. By evolving with the same viscosity the exact post-merger initial configuration previously evolved in Newtonian viscous hydrodynamics, we find that the Newtonian treatment provides a good estimate of the disk ejecta mass but underestimates the outflow velocity. We find that the inclusion of heavy nuclei causes a notable increase in ejecta mass. An approximate inclusion of r-process effects has a comparatively smaller effect, except for its designed effect on the composition. Diffusion of composition and entropy, modeling turbulent transport effects, has the overall effect of reducing ejecta mass and giving it a speed with lower average and more tightly-peaked distribution. Also, we find significant acceleration of outflow even at distances beyond 10 000 km, so that thermal wind velocities only asymptote beyond this radius and at higher values than often reported.

79 ASTRONOMY AND ASTROPHYSICS↗